Isomorphisms of Landau-Ginzburg B-Models

• Main Author: Cordner, Nathan James
• Format: Others
• Published: BYU ScholarsArchive 2016
• Subjects: Algebraic Geometry; Mirror Symmetry; FJRW Theory; Mathematics
• Online Access: https://scholarsarchive.byu.edu/etd/5882; https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=6881&context=etd

Landau-Ginzburg mirror symmetry predicts isomorphisms between graded Frobenius algebras (denoted A and B) that are constructed from a nondegenerate quasihomogeneous polynomial W and a related group of symmetries G. In 2013, Tay proved that given two polynomials W1, W2 with the same quasihomogeneous weights and same group G, the corresponding A-models built with (W1, G) and (W2, G) are isomorphic. An analogous theorem for isomorphisms between orbifolded B-models remains to be found. This thesis investigates isomorphisms between B-models using polynomials in two variables in search of such a theorem. In particular, several examples are given showing the relationship between continuous deformation on the B-side and isomorphisms that stem as a corollary to Tay's theorem via mirror symmetry. Results on extending known isomorphisms between unorbifolded B-models to the orbifolded case are exhibited. A general pattern for B-model isomorphisms, relating mirror symmetry and continuous deformation together, is also observed.